Finite Group DatabasebetaFinite Group Databasebeta| order | 20532 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C29 · Schur multiplier (H2) = C2 |
| Fitting, socle | C2×C3×C59 ⋊ C2×C29 |
| derived, Sylow | C59 ⋊ C22×C3×C29 |
| Hall | C3×C59⋊C29 ⋊ C22 |
| Hall | C59⋊C29 ⋊ C22×C3 |
| Hall | C2×C3×D59 ⋊ C29 |
| Hall | C2×D59 ⋊ C3×C29 |
| Hall | C3×C59 ⋊ C22×C29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | AGL(1,𝔽59) |
| commutator, cosocle, hypocenter | C59 | C22×C3×C29 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C59 | C2×C29 |
| LCS | G ▷ C59 | |
| UCS | C1 ◁ C2×C3 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 354 |
354 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20532, 16);